On Wednesday, he returned to the grand atrium that now bears his name at the center of the new terminal: Villaraigosa Pavilion. This time, it was Mayor Eric Garcetti’s turn to celebrate the opening/reopening of the $2-billion terminal — now the finest, by far, at LAX.

“It’s a great thing,” Villaraigosa joked as Garcetti prepared to take the stage for an event that would conclude with a Singapore Airlines jet rolling through a ribbon. “It’s so great, we ought to do it twice.”

It was also an occasion for Garcetti and Villaraigosa to join their predecessors James K. Hahn and Richard Riordan in a rare gathering of every living mayor of Los Angeles in a world-class air terminal with luxury shops and high-end restaurants.

In remarks to invited guests and world travelers passing by, Garcetti paid tribute to the former mayors for the part each of them played in modernizing LAX, ignoring, for the occasion, the lurching nature of the progress.

Hahn and Riordan were left off the speaking program. But Riordan said in a brief interview that he was honored to be included. He also joked that the point of staging two openings of the same building might be “to have the current mayor show they can put on a better show than the last mayor.”

Garcetti, setting aside competition for the limelight, saved his kindest words for Villaraigosa, calling him “a man whose name adorns this pavilion here, and who is responsible in large measure, more than anybody else, for making this day possible.”

“He happens to be a man who is now in the private sector, though I think we probably haven’t heard the last of him in the public sector,” Garcetti said.

Villaraigosa, who is weighing a run for California governor in 2018, is working as an advisor to Banc of California Inc. and Herbalife, a company that is fighting allegations that it operated an illegal pyramid scheme. After the event, Villaraigosa said he was proud to work for Herbalife and called it “one of the great health and nutrition companies anywhere.”

“It was still wrapped up a little bit in June,” he said, recalling that much of the building was still a construction site when Villaraigosa’s dinner gala took place. “It was, I think, an important milestone to do a pre-opening, because Mayor Villaraigosa was so involved. But today’s the day it actually opens.”

An airport spokeswoman played down the cost of Wednesday's event. The main expense was the $999 rental of 32 international flags placed behind the dignitaries who spoke, and the Westfield Group, which runs a retail franchise in the terminal, picked up the cost of Villaraigosa’s event in June, said Nancy Castles, a spokeswoman for Los Angeles World Airports.

Gina Marie Lindsey, executive director of the agency, said the June celebration marked “architectural completion” and the opening of the north gates. The one on Wednesday, she said, marked the opening of the south gates and Villaraigosa Pavilion, a name chosen by the airport commission appointed by the former mayor.

“I think everybody wanted to take any opportunity to celebrate the milestone achievements,” she said.

[For the record, 5:26 p.m. PDT, Sept. 18: An earlier version of this post said Gina Marie Lindsey, executive director of Los Angeles World Airports, said the June celebration marked the opening of the south gates. It marked the opening of the north gates. The Wednesday event marked the opening of the south gates.]